Is the Aguirre-Gratton time-reversed de Sitter model true?

In 2002, Anthony Aguirre and Steve Gratton published this model in a paper titled, “Steady-State Eternal Inflation.”1 Two prominent features of the model include:A) It is a de Sitter-like space featuring its quintessential bounce phase in the middle (This geometry produces an hourglass shape).B) A hypersurface representing its low entropy boundary condition. From this surface evolves two opposite-pointing thermodynamic arrows of time.2 Two interpretations (foliations) are offered, corresponding to two ways the surface could be oriented: (1) a surface cutting through the middle horizontally at the bounce phase and (2) a surface cutting diagonally from one corner to the other. Since opposite arrows of time evolve from this boundary,

• Sean Carroll: “...there is no place for God to have created such a universe. [God and Cosmology: William Lane Craig and Sean Carroll in Dialogue, ed. Stewart (Fortress, 2016), 231-232.]

Consequently, while there may be a thermodynamic beginning.3, Aguirre-Gratton claims there is neither an initial cosmic singularity nor literal initial conditions (just boundary conditions). This beginningless hourglass geometry is intended as a backdrop within which an inflationary bubble yields our universe.

• Andreas Albrecht: "there are actually two different 'back-to'back' coherent domains in this picture, with arrows of time pointing in opposite directions. The coherence must extend over infinitely many reheated regions, distributed throughout an infinitely large spacetime volume." [Science and Ultimate Reality (), 388.]
AG#1: Our Relative perspective• Sean Carroll: “on either side of the bounce, the arrow points towards a ‘future’ in which the universe is expanding and emptying out. To observers on either side, observers on the other side experience time ‘running backward.’ But this mismatch of arrows is completely unobservable—people on one side of the bounce can’t communicate with people on the other,” [From Eternity to Here, ]
From our perspective, observers on the other side of the throat are in a past-eternal universe. Pick a time in their civilization, and from our perspective pressing “play” results in them walking backwards and stirring their eggs backwards (unscrambling them). Their adults progressively become teenagers, unlearning everything, and then regress into babies. Ironically, they view us the same way. Observes on both sides see their universe as being an unfathomably highly improbable “fluctuation” out from the previous universe.• Victor Stenger: “The Hartle-Hawking model has another interpretation that is mathematically equivalent, namely one in which two universes start at t=0 and proceed in opposite directions in time. Hawking mentions the possibility in 300 Years of Gravitation, published in 1987. I have promoted the notion in several popular books and articles going back to 2000. So the well-established equations of physics and cosmology allow for the existence of two mirror universes: ours that expands along the positive time axis and a prior universe that exists at negative times. From our point of view, our universe appears by quantum tunneling from the earlier universe.
No singularity; Describing the geometry• Sean Carrol: “…we have attempts to “smooth out” the singularity in some semi-classical way. Aguirre and Gratton have presented a proof by construction that such a universe is conceivable; essentially, they demonstrate how to take an inflating spacetime, cut it near the beginning, and glue it to an identical spacetime that is expanding the opposite direction of time. This can either be thought of as a universe in which the arrow of time reverses at some special midpoint, or (by identifying events on opposite sides of the cut) as a one-way spacetime with no beginning boundary.[article]

Some argue that this middle hypersurface functions as a beginning.

• Alexander Vilenkin: “Even though the spacetime has no boundary in the AG model, it does include a surface B on which the low-entropy (vacuum) boundary condition must be enforced by some unknown mechanism. This Cauchy surface of minimum entropy plays the role of the beginning of the universe in this scenario.” [https://arxiv.org/pdf/1305.3836.pdf]• Aron Wall: “This kind of bounce evades both the singularity and thermodynamic arrow constraints, but still has in some sense a thermodynamic ‘beginning’ in time at the moment of lowest entropy [t0t0]. That is, both the past and the future would be explained in terms of the low entropy state at t0t0, while the state at t0t0 would itself have no explanation in terms of anything to the future or the past. (Thus the moment t0t0 would seem to raise the same sorts of philosophical questions that any other sort of beginning in time would.)” [The Generalized Second Law implies a Quantum Singularity Theorem (), ]

During the past-infinite contracting phase, the whole space becomes thermalized1 This is relevant because if a space is entirely thermalized, it is no longer de Sitter; instead of a bounce and expansion, the thermalized space ends in a big crunch.2

• Arvin Borde, Alan Guth, Alexander Vilenkin:“If thermalized regions were able to form all the way to past infinity in the contracting space-time, the whole universe would have been thermalized before inflationary expansion could begin.” [“Inflationary spacetimes are not past-complete.” Physical Review Letters 90, 151301 (2003)]

• Alexander Vilenkin: “Then bubbles nucleating at τ → −∞ will fill the space, the energy in the bubble walls will thermalize, and the universe will contract to a big crunch and will never get to the bounce and to the expanding phase.” [“Arrows of time and the beginning of the universe.” Physical Review D 88, 043516 (2013)]

The model requires “acausal fine-tuning.” (That is to say, the entropic evolution is extraordinarily fine-tuned1, and yet logically eliminates any hope of explaining it.) This is relevant because it means the prior probability of the model being true irresolvably something like 1 over infinity; i.e. the chances of it being true are virtually nil and the model would correspondingly require infinitely good evidence.

The model puts the low-entropy problem in the middle of the hourglass, and yet they provide no mechanism to bring about this unnatural state. In fact, worse, the model in principle removes any hope of ultimately increasing the probability of the highly improbable state.

• Alexander Vilenkin: “The Aguirre-Gratton model can avoid singularities by postulating a small “initial” closed universe and then allowing it to evolve in both directions of time. I put "initial" in quotation marks, because Aguirre and Gratton do not think of it that way. But this model requires that a very special condition is enforced at some moment in the history of the universe. At that moment, the universe should be very small and have very low entropy. Aguirre and Gratton do not specify a physical mechanism that could enforce such a condition.” [E-mail to William Lane Craig: reasonablefaith.org/honesty-transparency-full-disclosure-and-bgv-theorem]• Andreas Albrecht: “In the Aguirre-Gratton construction, the arrow of time is put in by hand. One simply declares 'the universe is in this state,' and it happens to have an arrow of time. [389.] ... “The eternally inflation state that emerges from that approach has specific global properties that reflect an arrow of time. In particular, an array of regions of reheating (or decay of the potential-dominated state) must be organized coherently to be pointing in a commonly agreed ‘forward direction.’ In fact, there are actually two different ‘back-to-back’ coherent domains in this picture, with arrows of time pointing in opposite directions. The coherence must extend over infinitely many reheated regions, distributed throughout an infinitely large spacetime volume.” [Science and Ultimate Reaity (Cambridge, 2004), 388.]• Sean Carroll: “Why is the entropy so low in the middle of the history of the universe? In other words, the bouncing-entropy model doesn’t, by itself, explain anything at all about the arrow of time. Rather, it takes the need for a Past Hypothesis and replaced it with the need for a “Middle Hypothesis.” There is just as much fine-tuning as ever; we are still stuck trying to explain why the configuration of our coming patch of space found itself in such a low-entropy state near the cosmological bounce.” [From Eternity to Here (), none-given.]

The Aguirre-Gratton model undercuts causal reasoning (in life and science) (After all, the model yields two mirror halves, so there's a 50% chance we are the half experiencing time in thermodynamic reverse.) This is relevant because its an absurd conclusion and even undercuts justification for belief in the model itself.1

To see how the Aguirre-Gratton model may be self-defeating, consider that knowledge requires justified true belief (or something like it), and justification (or anything like it) requires the belief to be formed in the right way. However, believing the Aguirre-Gratton model means having a belief which entails a 50% likelihood that your belief in the model itself was formed in a terrible way: by spontaneously forming and being grounded in a reasoning process you haven't done yet, and on the basis of false memories of events you haven't experienced yet.